The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C*-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting....

Historically, inverse spectral theory has been concerned with the relationship between the geometry and the spectrum of compact Riemannian manifolds, where spectrum means the eigenvalue spectrum of the Laplace operator as it acts on smooth...

We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian...

The processes affecting gas transport through the firn column are important to understand in order to accurately interpret climate records from ice cores. Historically, density measurements have been used to estimate open and closed porosity in the...

This thesis contains material relating to two separate subjects. The first section determines when the C*-algebra affiliated to a directed graph has continuous trace. We use groupoid methods and the focus is on producing conditions on a graph that...

This work describes the effect of triaxial compressive confinement on the strength of columnar S2 ice loaded under conditions leading to brittle failure. Cubes of columnar S2 ice were tested at -10 °C under triaxial (proportional) loading where...

The accelerated expansion of space in the Universe has been known for two decades. However, finding a plausible theory that describes this expansion is more difficult: Taking general relativity for granted requires us to stipulate the existence of...

'Orthogonal modular forms are algebraic modular forms arising from lattices in quadratic spaces. In this thesis, we define orthogonal modular forms, establish their basic properties, and then apply them to a case of ternary quadratic spaces to...

Magnetic fields at all scales are prevalent in our universe. However, current cosmological models predict that initially the universe was bereft of large-scale fields. Standard magnetohydrodynamics (MHD) does not permit magnetogenesis; in the MHD...

The thesis is dedicated to the understanding and characterization of brittle compressive fracture of columnar S2 ice. The work quantifies the strength of fresh-water S2 ice and investigates its characteristic brittle failure modes under biaxial...

Spectral theory is the subfield of differential geometry which provided the solution to Kac''s famous question, "Can you hear the shape of a drum?" That is, can we use the Laplace spectrum of a manifold to draw conclusions about its geometry or...

We study the effects of anisotropic pressure on the properties of spherically symmetric, gravitationally bound spheres. We consider the full general-relativistic and Newtonian treatment of this problem and obtain exact solutions for various forms...

In this thesis we review the methods for computation of cosmological correlations in the early universe known as the in-in formalism which are then applied to the problem of magnetogenesis from inflation. For this computation, a power-law single...

Ultra high molecular weight polyethylene (UHMWPE) is the most common bearing material in joint arthroplasty due to its biocompatibility, its wear resistance, and its mechanical toughness. Despite the favorable properties of UHMWPE and its success...

Cosmic acceleration could be an effect of a ""dark energy"" fluid pervading the Universe. It could also be an indication that general relativity is not the correct theory of gravity at cosmological length scales. Unfortunately, observations of the...

The condition ""every cycle has an entry"" first appeared in the literature in Kumjian, Pask, and Raeburn's paper on Cuntz-Krieger algebras of directed graphs, where it was called Condition (L). It provides a necessary condition for simplicity of...

The manufacture of bulk parts from metastable powder materials requires new approaches to cold consolidation. One potential technique is equal-channel angular extrusion (ECAE), a simple shear process. This thesis describes an investigation into the...

Multiresolution image transformations have become commonplace tools for analyzing images for a number of applications, including enhancement and restoration. Powerful models for these applications have been developed in the transform domain of...

Magnetic resonance elastography (MRE) is a technique to produce images of the mechanical properties of tissue, which are indicative of a variety of diseases. Tissue motions measured using MRI are used to solve an inverse problem to recover...